Page 111 - Biodegradable Polyesters

4.4 Mathematical Modeling of the Synthesis of Aliphatic Polyesters 89

based on functional group analysis, which had originally been developed for PET
synthesis by Kang et al. [38, 39] and extended by our group in the production of
PPT [7]. According to this approach, the polymerization reaction is regarded as a
reaction between two functional groups. The molecular structures of the compo-
nents considered in the reaction scheme are presented in Table 4.1.
Using the notation for the molecular structure of the components illustrated
in Table 4.1, a general esterification reaction mechanism can be derived includ-
ing different dicarboxylic acids such as succinic, glutaric, adipic, pimelic, suberic,
azelaic, and sebacic acid with a = 2, 3, 4, 5, 6, 7, or 8 methylene groups denoted
as SA and various glycols (G) including ethylene, propylene, and butylene with
g = 2, 3, and 4 methylene groups. Five different oligomeric segments are used:
tSA, tG, bSA, bG, and bDG (the terms t and b refer to the terminal functional
group and bound monomeric repeating unit, respectively).
On the basis of these functional groups, the following mechanism is assumed
to represent the kinetics of the esterification process [7].

k 1
SA + G ⇌ tSA + tG + W (4.6)
k ′
1
k 2
tSA + G ⇌ bSA + tG + W (4.7)
k ′
2
k 3
SA + tG ⇌ tSA + bG + W (4.8)
k ′
3
k 4
tSA + tG ⇌ bSA + bG + W (4.9)
k ′
4
Table 4.1 Molecular structures of components considered.

Material Symbol Description Molecular structure a) ,b)

Monomers SA Dicarboxylic acid HOOC–(CH ) –COOH
2 a
G Glycol HO– (CH ) –OH
2 g
Product W Water H O
2
Oligomers tSA Acid end group HOOC– (CH ) –CO–
2 a
tG Glycol end group HO– (CH ) –O–
2 g
bSA Acid repeating unit –OC– (CH ) –CO–
2 a
bG Glycol repeating unit –O– (CH ) –O–
2 g
bDG Di-alkylene glycol repeating unit –O– (CH ) –O– (CH ) –O–
2 g
2 g
a) g = 2, 3, 4 for ethylene glycol, propylene glycol, and butylene glycol, respectively.
b) a = 2, 3, 4, 5, 6, 7, and 8 for succinic, glutaric, adipic, pimelic, suberic, azelaic, and
sebacic acid.